81586 ÷ 3 = 27195 R1
Alright, let's work through the division of 81586 by 3 step by step.

Step 1:
3 goes into 8 2 times with a remainder of 2.
Write down 2 as next digit of of the result. 
Result so far: 2
Subtract 6 from 8 to get 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 3

Step 2:
3 goes into 21 7 times with a remainder of 0.
Write down 7 as next digit of of the result. 
Result so far: 27
Subtract 21 from 21 to get 0.
Bring next digit (5) of the dividend behind the 0 and repeat the process: 5 / 3

Step 3:
3 goes into 5 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 271
Subtract 3 from 5 to get 2.
Bring next digit (8) of the dividend behind the 2 and repeat the process: 28 / 3

Step 4:
3 goes into 28 9 times with a remainder of 1.
Write down 9 as next digit of of the result. 
Result so far: 2719
Subtract 27 from 28 to get 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 3

Step 5:
3 goes into 16 5 times with a remainder of 1.
Write down 5 as next digit of of the result. 
Result so far: 27195
Subtract 15 from 16 to get 1.

The final result is 27195 with a remainder of 1.